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3---48

UNIVERSIDAD TCNICA DE AMBATO

FACULATD DE INGENIERIA EN SISTEMAS ELECTRONICA E INDUSTRIALSIMULACION DE SISTEMAS DE MANUAFACTURA

Nombre:Mnica Herrera GalarzaFecha:5/21/15

Programe en una hoja de clculo la generacin automtica de nmeros pseudo aleatorios con el mtodo de cuadrados medios. Genere una muestra de 50 nmeros con la semilla 5 735, y determine con un nivel de aceptacin de 90% si son uniformes entre 0 y 1.

Generacin de la muestraiSEMILLA57351573557353289022532890232000089022890289027924560479245679000024563245624566031936603196000031943193191017611017610000176517617630976309730973097630973097959140995914900005914759145914349753963497533400009753897539753951210099512109500001210912101210146410014641100004641104641464121538881215388210000538810538853882903054429030529000030510305305930259302930293021393029302865272048652728600005272145272527227793984277939270000793915793979396302772163027763000027716277277767297672767200076721776727672588595845885955800008595188595859573874025738740730000874019874087407638760076387676000038762038763876150233761502331500002332123323354289542854285428225428542829463184294631290000463123463146312144616121446121000044612444614461199005211990051900009005259005900581090025810900810000900269009008100008100080000100027100010001000000100001000002800000029000000300000003100000032000000330000003400000035000000360000003700000038000000390000004000000041000000420000004300000044000000450000004600000047000000480000004900000050000000

# Muestras=26 Muestras=93993

Muestras Ordenadasri/10000Acumuladari/100i/n(i-1)/n(i/n)-riri-(i-1)/n01760.01760.01760.00020.040.0000.03830.000202330.02330.04090.00040.080.0380.0765-0.038102770.02770.06860.00070.120.0770.1147-0.076203050.03050.09910.00100.150.1150.1529-0.114403190.03190.13100.00130.190.1540.1910-0.152509000.09000.22100.00220.230.1920.2286-0.1901010000.10000.32100.00320.270.2310.2660-0.2276012100.12100.44200.00440.310.2690.3033-0.2648024560.24560.68760.00690.350.3080.3393-0.3008030970.30970.99730.01000.380.3460.3746-0.3362038760.38761.38490.01380.380.3460.3708-0.3323044610.44611.83100.01830.380.3460.3663-0.3278046310.46312.29410.02290.500.4620.4771-0.4386046410.46412.75820.02760.540.5000.5109-0.4724052720.52723.28540.03290.580.5380.5441-0.5056053880.53883.82420.03820.620.5770.5771-0.5387054280.54284.36700.04370.650.6150.6102-0.5717059140.59144.95840.04960.690.6540.6427-0.6043076720.76725.72560.05730.730.6920.6735-0.6351079390.79396.51950.06520.770.7310.7040-0.6656085950.85957.37900.07380.810.7690.7339-0.6954087400.87408.25300.08250.850.8080.7636-0.7252089020.89029.14320.09140.880.8460.7932-0.7547090050.900510.04370.10040.920.8850.8226-0.7842093020.930210.97390.10970.960.9230.8518-0.8133097530.975311.94920.11951.000.9620.8805-0.8420D (+)D (-)0.88051-0.84205

VALOR:0.2332

4---48




Realice las pruebas de media, varianza y uniformidad a los 50 nmeros de la tabla siguiente, con un nivel de aceptacin de 95 por ciento.

0.87970.38840.62890.8750.59990.85890.99960.24150.38080.96060.98480.34690.79770.58440.81470.64310.73870.56130.03180.74010.45570.15920.85360.88460.3410.14920.86810.52910.31880.59920.9170.22040.59910.54610.57390.32540.08560.22580.46030.50270.83760.62350.36810.20880.15250.20060.4720.42720.6360.0954

Regla de Sturges: No.Intervalos= 1+3.3* log (N)Probabilidad de Poison:

N =50No. Intervalos = 6.6066010143

Determinacin del alcance de intervalo:0.0004215867Vmax =1.000Vmin =0.032# Intervalos =7

Alcance =0.1382571429Alcance =0.1383

Determinacin de la Media:

Suma Xi =26.69330.533866

Determinacin de la Varianza:

(Xi - X)^2 =3.6464

Sx =0.0744

DATOS ORDENADOSIntervaloFrecuencia OiEi(Ei-Oi)/EiDATOS0,0318-0,170167.14285714290.18285714290.03180.25207026840,1701-0,308457.14285714290.64285714290.08560.20094240680,3084-0,446787.14285714290.10285714290.09540.19225243320,4467-0,58597.14285714290.48285714290.14920.14796793160,585-0,723377.14285714290.00285714290.15250.1454400260,7233-0,861677.14285714290.00285714290.15920.14037461160,8616-0,999987.14285714290.10285714290.20060.1110662268Sumatoria50501.52000.20880.10566790440.22040.09826093320.22580.0949046604Grados de Libertad= I-1intervalos -160.24150.085477878Probabilidad95%5%0.31880.0462533844Indice Chi-Cuadrado1.520012.590.32540.04345807320.3410.037197294El valor optenido es inferior al de la tabla, por lo tanto no se puede decir que los numero ri tengan una secuencia de distribucion uniforme.0.34690.03495628520.36810.02747836680.38080.02342920040.38840.021160357295% ==> z =1.960.42720.01137763560.45570.0061099236Prueba de la MediaPrueba de la Varianza0.46030.0054119564L. Superior0.5800L. Superior0.12360.4720.003827402L. Inferior0.4200L. Inferior0.12360.50270.00097131960.52910.00002271480.54610.00014967080.02500.56130.00075262444059.34200.57390.00160272124972.69400.58440.00255368524262.30910.59910.00425547484363.79270.59920.00426853164465.27620.59990.00436048924566.75980.62350.0080342544668.24330.62890.00903146124769.72690.6360.0104313544871.21040.64310.01193206684972.69400.73870.04195696765074.17750.74010.04253246285175.66110.79770.06960837960.81470.07886773560.83760.09225434280.85360.10222983080.85890.10564710120.86810.11171236680.8750.1163724060.87970.11960115560.88460.12301433880.9170.1467916620.96060.18210190680.98480.20334147240.99960.2169081588

2--90




A partir de la prueba Chi-cuadrada determine, con un nivel de confianza de 90%, qu tipo de distribucin siguen los datos.

n100DATOSriIntervalo7.6ValoresIntervaloFrecuencia OiEi(Ei-Oi)/Ei18.7999.690Intervalos89.699,69-12,1666312.57.2217.23911.266Alcance2.476612.166612,1666-14,6432912.50.9818.69211.528Media19.838114.643214,6432-17,11981612.50.9826.64612.612Varianza18.858117.119817,1198-19,59642112.55.7814.22312.90119.596419,5964-22,0731812.52.429.69013.03022.07322,073-24,54961812.52.4222.77613.23824.549624,5496-27,0262912.50.9820.28913.55027.026227,0262-29,5028612.53.3828.82313.764Suma10012.512.521.77713.91414.88914.22313.23814.51318.51914.88113.55014.889Grados de Libertad8-1=716.61115.195Probabilidad90%=0,0125.79115.537Indice Chi-Cuadrado12.017921.29115.653En base al calculo se dice que los numeros aleatorios no siguen un distribucion uniforme23.31915.78125.77515.89222.47216.08920.97716.24112.61216.30725.37116.35622.15616.61113.91416.64014.88116.71516.24116.90623.44817.05425.21617.23920.85417.38025.10617.38616.08917.45419.65917.72823.60917.90518.54817.94717.38618.18719.03618.28417.45418.38420.45218.47515.89218.51924.79318.53816.90618.54819.25518.69227.67618.70919.87018.75523.03118.79920.52619.03616.30719.06320.00819.25524.95319.65926.93319.66211.52819.87017.94719.89819.66220.00820.11220.11221.86720.28922.23120.45224.44520.52621.81520.53918.75520.55511.26620.85417.72820.97727.88921.29117.90521.77718.70921.81523.49821.86720.55521.94915.19522.15619.89822.23116.64022.38319.06322.47218.38422.55423.46322.70122.70122.77628.77822.84522.38323.03016.35623.03113.76423.31315.78123.31916.71523.44824.38023.46320.53923.49829.50323.60918.47524.38013.03024.44514.51324.79327.53924.95322.84525.10612.90125.21618.28425.37115.65325.77518.53825.79117.38026.64623.03026.93317.05427.53915.53727.67621.94927.88922.55428.77823.31328.82318.18729.503

5--91




Determine, con un nivel de confianza de 95%, qu tipo de distribucin siguen los datos; emplee la prueba de Kolmogorov-Smirnov.

12,5618,3224,05711,96315,15415,3303,18621,5003,6433,7752,6957,42215,5845,5999,5797,9589,0517,16027,33416,67512,08211,1439,04919,2048,4237,10311,11813,5283,1781,36810,33520,5996,2651,7846,93416,1344,4493,3721,31317,58313,2607,50810,66325,9982,0050.18917,90115,33410,9621,6692,5494,36710,25712,29913,23410,16515,4977,6036,93611,1574,5941,54411,47510,3175,54214,6246,64531,0663,14016,4322,5003,7064,6883,7795,27115,6965,0781,99216,8772,83124,9308,18516,25618,99312,83110,21211,55521,12719,1717,8447,80514,4054,6887,4198,2310.8913,72410,7846,62010,745iMuestras Ordenadasri/1000Acumuladai/n(i-1)/n(i/n)-riri-(i-1)/n10.1890.001890.001890.010.000.008110.0018920.8910.008910.01080.020.010.01109-0.0010931.3130.013130.023930.030.020.01687-0.0068741.3680.013680.037610.040.030.02632-0.0163251.5440.015440.053050.050.040.03456-0.0245661.6690.016690.069740.060.050.04331-0.0333171.7840.017840.087580.070.060.05216-0.0421681.9920.019920.10750.080.070.06008-0.0500892.0050.020050.127550.090.080.06995-0.05995102.5000.0250.152550.10.090.075-0.065112.5490.025490.178040.110.100.08451-0.07451122.6950.026950.204990.120.110.09305-0.08305132.8310.028310.23330.130.120.10169-0.09169143.1400.03140.26470.140.130.1086-0.0986153.1780.031780.296480.150.140.11822-0.10822163.1860.031860.328340.160.150.12814-0.11814173.3720.033720.362060.170.160.13628-0.12628183.6430.036430.398490.180.170.14357-0.13357193.7060.037060.435550.190.180.15294-0.14294203.7240.037240.472790.20.190.16276-0.15276213.7750.037750.510540.210.200.17225-0.16225223.7790.037790.548330.220.210.18221-0.17221234.0570.040570.58890.230.220.18943-0.17943244.3670.043670.632570.240.230.19633-0.18633254.4490.044490.677060.250.240.20551-0.19551264.5940.045940.7230.260.250.21406-0.20406274.6880.046880.769880.270.260.22312-0.21312284.6880.046880.816760.280.270.23312-0.22312295.0780.050780.867540.290.280.23922-0.22922305.2710.052710.920250.30.290.24729-0.23729315.5420.055420.975670.310.300.25458-0.24458325.5990.055991.031660.320.310.26401-0.25401336.2650.062651.094310.330.320.26735-0.25735346.6200.06621.160510.340.330.2738-0.2638356.6450.066451.226960.350.340.28355-0.27355366.9340.069341.29630.360.350.29066-0.28066376.9360.069361.365660.370.360.30064-0.29064387.1030.071031.436690.380.370.30897-0.29897397.1600.07161.508290.390.380.3184-0.3084407.4190.074191.582480.40.390.32581-0.31581417.4220.074221.65670.410.400.33578-0.32578427.5080.075081.731780.420.410.34492-0.33492437.6030.076031.807810.430.420.35397-0.34397447.8050.078051.885860.440.430.36195-0.35195457.8440.078441.96430.450.440.37156-0.36156467.9580.079582.043880.460.450.38042-0.37042478.1850.081852.125730.470.460.38815-0.37815488.2310.082312.208040.480.470.39769-0.38769498.3220.083222.291260.490.480.40678-0.39678508.4230.084232.375490.50.490.41577-0.40577519.0490.090492.465980.510.500.41951-0.40951529.0510.090512.556490.520.510.42949-0.41949539.5790.095792.652280.530.520.43421-0.424215410.1650.101652.753930.540.530.43835-0.428355510.2120.102122.856050.550.540.44788-0.437885610.2570.102572.958620.560.550.45743-0.447435710.3170.103173.061790.570.560.46683-0.456835810.3350.103353.165140.580.570.47665-0.466655910.6630.106633.271770.590.580.48337-0.473376010.7450.107453.379220.60.590.49255-0.482556110.7840.107843.487060.610.600.50216-0.492166210.9620.109623.596680.620.610.51038-0.500386311.1180.111183.707860.630.620.51882-0.508826411.1430.111433.819290.640.630.52857-0.518576511.1570.111573.930860.650.640.53843-0.528436611.4750.114754.045610.660.650.54525-0.535256711.5550.115554.161160.670.660.55445-0.544456811.9630.119634.280790.680.670.56037-0.550376912.0820.120824.401610.690.680.56918-0.559187012.2990.122994.52460.70.690.57701-0.567017112.5610.125614.650210.710.700.58439-0.574397212.8310.128314.778520.720.710.59169-0.581697313.2340.132344.910860.730.720.59766-0.587667413.2600.13265.043460.740.730.6074-0.59747513.5280.135285.178740.750.740.61472-0.604727614.4050.144055.322790.760.750.61595-0.60595n=100I7714.6240.146245.469030.770.760.62376-0.613760,05=0.1367815.1540.151545.620570.780.770.62846-0.618467915.3300.15335.773870.790.780.6367-0.62678015.3340.153345.927210.80.790.64666-0.636668115.4970.154976.082180.810.800.65503-0.645038215.5840.155846.238020.820.810.66416-0.654168315.6960.156966.394980.830.820.67304-0.663048416.1340.161346.556320.840.830.67866-0.668668516.2560.162566.718880.850.840.68744-0.677448616.4320.164326.88320.860.850.69568-0.685688716.6750.166757.049950.870.860.70325-0.693258816.8770.168777.218720.880.870.71123-0.701238917.5830.175837.394550.890.880.71417-0.704179017.9010.179017.573560.90.890.72099-0.710999118.9930.189937.763490.910.900.72007-0.710079219.1710.191717.95520.920.910.72829-0.718299319.2040.192048.147240.930.920.73796-0.727969420.5990.205998.353230.940.930.73401-0.724019521.1270.211278.56450.950.940.73873-0.728739621.5000.2158.77950.960.950.745-0.7359724.9300.24939.02880.970.960.7207-0.71079825.9980.259989.288780.980.970.72002-0.710029927.3340.273349.562120.990.980.71666-0.7066610031.0660.310669.8727810.990.68934-0.67934D (+)D (-)0.74500-0.73500Valor de la tabla =0.136